Background: Rapid changes in the expression of many messenger RNA (mRNA) species follow exposure of cells to ionizing radiation. One of the hypothetical mechanisms of this response may include microRNA (miRNA) regulation, since the amounts of miRNAs in cells also vary upon irradiation. To address this possibility, we designed experiments using cancer-derived cell lines transfected with luciferase reporter gene containing sequences targeted by different miRNA species in its 3′- untranslated region. We focus on the early time-course response (1 h past irradiation) to eliminate secondary mRNA expression waves. Results: Experiments revealed that the irradiation-induced changes in the mRNA expression depend on the miRNAs which interact with mRNA. To identify the strongest interactions, we propose a mathematical model which predicts the mRNA fold expression changes, caused by perturbation of microRNA-mRNA interactions. Model was applied to experimental data including various cell lines, irradiation doses and observation times, both ours and literature-based. Comparison of modelled and experimental mRNA expression levels given miRNA level changes allows estimating how many and which miRNAs play a significant role in transcriptome response to stress conditions in different cell types. As an example, in the human melanoma cell line the comparison suggests that, globally, a major part of the irradiation-induced changes of mRNA expression can be explained by perturbed miRNA-mRNA interactions. A subset of about 30 out of a few hundred miRNAs expressed in these cells appears to account for the changes. These miRNAs play crucial roles in regulatory mechanisms observed after irradiation. In addition, these miRNAs have a higher average content of GC and a higher number of targeted transcripts, and many have been reported to play a role in the development of cancer. Conclusions: Our proposed mathematical modeling approach may be used to identify miRNAs which participate in responses of cells to ionizing radiation, and other stress factors such as extremes of temperature, exposure to toxins, and drugs.